Size-biased random closed sets

We indicate how granulometries may be useful in the analysis of random sets. We define a suitable size distribution function as a tool in exploratory data analysis and give a new Hanisch style estimator for it. New Markov random sets are constructed which favour certain sizes above others. A size-biased random set model is fitted to a data set concerning the incidence of heather (Diggle, Biometrics 37 (1981) 531–539)

Size-biased random closed sets

We indicate how granulometries may be useful in the analysis of random sets. After defining a size distribution function which may be used as a summary statistic in exploratory data analysis, we propose a Hanisch-type estimator and construct new Markov random set models which favour certain sizes above others. The models are illustrated by simulated realisations